Solution to Problem REF  is known on \(S^1\)  for every \(N\)  (equally spaced points), on \(S^2\)  for \(N=1-8\) , 10, 12, and 14, see the works by Fejes-Tóth [1]}, [2]}, [3]}, Schütte [4]}, and Wimmer [5]}, on \(S^3\)  for \(N=1-6\)  and 8, see the works by Galiev [6]}, Böröczky and Wintsche [7]}, and Dalla, Larman, Mani-Levitska, and Zong [8]}, and on \(S^{d-1}\) , \(d>4\) , for \(1\le N\le d+2\) , see [6]}, [7]}. For more information on optimal covering, see, among others, books by Fejes-Tóth [1]}, [2]}, Rogers [13]}, and Böröczky [14]}.
